FIG. 1 represents a simplified target tracking system 10. System 10 tracks a target, illustrated as being an aircraft 12, by the use of multiple radar systems 14, 16. Radar system 14 includes a radar antenna 14a, which transmits and receives radar signals illustrated by “lightning bolt” symbols 18. Portions of the transmitted signals 18 are reflected by target 12 and return to the radar antenna 14a. The returned signals allow the generation of measurements at an output port 14o of radar system 14. Radar system 16 includes a radar antenna 16a, which transmits and receives radar signals illustrated by “lightning bolt” symbols 20. Portions of the transmitted signals 20 are reflected by target 12 and return to the radar antenna 16a. The returned signals allow the generation of measurements at an output port 16o of radar system 16. These measurements include values of at least target position, possibly in the form of range and angles from the radar systems 14 and 16. A possible scenario is that radar system 14 has less accuracy (higher measurement noise) but provides more current data whereas radar system 16 is more accurate (less measurement noise) but provides data with time latency. The measurements are applied to a processing arrangement 22, which determines from the measurements various target parameters, which may include course (direction of motion), speed, and target type. The estimated position of the target, and possibly other information, is provided to a utilization apparatus or user, illustrated in this case as being a radar display 24. The operator (or possibly automated decision-making equipment) can make decisions as to actions to be taken in response to the displayed information. It should be understood that the radar tracking system 10 of FIG. 1 is only one embodiment of a general class of estimation systems for systems with distributed sensors such as nuclear, chemical, or manufacturing factories or facilities, control processes subject to external parameter changes, space station subject to vibrations, automobile subject to weather conditions, and the like.
State-of-the-art tracking systems utilize measurements fed to a processing site from multiple sensors. These sensors may have different measuring accuracies and may be geographically dispersed over a region of interest. Availability of reliable high bandwidth communication media allows such a topology of distributed multiple sensors for real-time processing of the measurements.
In spite of today's high bandwidth and fast switching communication network, physical distances, path diversity and relays may result in different delays from various sensors to the processing site. Let a sensor S1 measure a tracked object at time t1 and a sensor S2 measure that same object at time t2 where t2>t1. It is possible that the measurement from sensor S1 may arrive many sampling intervals after the measurement from sensor S2 has already been processed. A simple decision methodology is to throw out the late-arriving measurement from sensor S1, and not process it at all. However, if sensor S1 is the more accurate sensor, this methodology does not make good use of that sensor.
A difficulty is that accounting for measurements received out of sequence, as frequently happens in situations of multiple sensor tracking with variable communication delays between sensors, greatly complicates the design of a Kalman filter, particularly when more than one subsequent measurement is processed before an out-of-sequence measurement is received as indicated in Y. Bar-Shalom, “Update with Out-of-Sequence Measurements in Tracking: Exact Solution,” IEEE Transactions on Aerospace and Electronic Systems, pp. 769–778, Vol. AES-38, No. 3, July 2002, J. R. Moore and W. D. Blair, “Practical Aspects of Multisensor Tracking,” in Multitarget-Multisensor Tracking: Applications and Advances, Volume III, Y. Bar-Shalom and William Dale Blair, (ed.), Boston, Mass.: Artech House, 2000, pp. 43–44, and Portmann, Moore, and Bath. Currently, even with rapid communications, delays of up to one second are not uncommon. As described below, even such small delays may have a significant effect on multisensor fusion tracking performance. Unlike smoothing and filtering, “how to update the current state estimate with an “older” measurement is a nonstandard estimation problem” as quoted from Y. Bar-Shalom, M. Mallick, H. Chen, and R. Washburn, “One-Step Solution for the General Out-of-Sequence-Measurement Problem in Tracking,” Proceedings of 2002 IEEE Aerospace Conference Proceedings, Volume 4, pp. 1551–1559, March 2002. No one definitive approach has yet been developed for this. The above is the opinion of Y. Bar-Shalom; Y. Bar-Shalom, M. Mallick, H. Chen, and R. Washburn; S. Challa and J. A. Legg, “Track-to-Track Fusion of Out-of-Sequence Tracks,” Proceedings of the Fifth International Conference on Information Fusion, pp. 919–926, July 2002; S. Challa, R. J. Evans, X. Wang, and J. Legg, “A Fixed-Lag Smoothing Solution to Out-of-Sequence Information Fusion Problems,” Communications in Information and Systems, pp. 325–348, Vol. 2, No. 4, December 2002; M. L. Hernandez, A. D. Marrs, S. Maskell, and M. R. Orton, “Tracking and fusion for wireless sensor networks,” Proceedings of the Fifth International Conference on Information Fusion, Vol. 2, pp. 1023–1029, July 2002; M. Ito, S. Tsujimichi, and Y. Kosuge, “Target Tracking with Time-Delayed Data in Multiple Radar System,” Proceedings of the 37th SICE Annual Conference, pp. 939–944, July 1998; J. R. Moore and W. D. Blair; M. Mallick, S. Coraluppi, and C. Carthel, “Advances in Asynchronous and Decentralized Estimation,” Proceedings of 2001 IEEE Aerospace Conference Proceedings, Vol. 4, pp. 1873–1888, March 2001; M. Mallick, J. Krant, and Y. Bar-Shalom, “Multi-sensor Multi-target Tracking using Out-of-sequence Measurements,” Proceedings of the Fifth International Conference on Information Fusion, Vol. 1, pp. 135–142, July 2002. This is particularly true when it is desired that during target maneuvers, the state estimate at the time of the current update (as opposed to at the past time of the “older” measurement, as in smoothing) have minimal covariance.
Filters without plant noise can optimally process out-of-sequence measurements in the order that they are received as stated by G. J. Portmann, J. R. Moore, and W. G. Bath supra. An optimal reduced state estimator has been developed that approximates the higher derivatives of target motion with constant parameters belonging to a multivariate Gaussian distribution as in the patent application entitled “REDUCED STATE ESTIMATOR FOR SYSTEMS WITH PHYSICALLY BOUNDED PARAMETERS,” filed Mar. 16, 2005, in the names of P. Mookerjee and F. Reifler. This estimator does not need the white plant noise required by Kalman filter to cope with the reduced state. Among all estimators (including reduced state Kalman filters) with the same reduced states, the optimal reduced state estimator has minimal covariance. This covariance is the minimal covariance achievable by linearly weighting the predicted states with a new measurement at each successive update of the filter. Since parameter uncertainty is included in the total error covariance that is minimized, the optimal reduced state estimator does not need white plant noise to cope with the reduced state.
Algorithms in the prior art are based on the Kalman filter. These algorithms either set the white process noise to zero while processing an out-of-sequence measurement (which does not achieve good performance), or using a non-zero white process noise, provide solutions for processing measurements which are late by at most a few update intervals. No algorithm exists in the prior art for providing an optimal solution when delays occur that are longer than a few update intervals. It is common, however, that delays may be large such as ten or more update intervals, which the current algorithms do not address.
In the prior art, the solutions are approximate as stated in P. J. Lanzkron and Y. Bar-Shalom, “A Two-Step Method for Out-Of-Sequence Measurements,” Proceedings of the IEEE Aerospace Conference, Big Sky, Mont., March 2004, pp. 2036–2041. These approximations are not available for delays larger than a few update intervals.
Improved or alternative estimators are desired for coping with out-of-sequence measurements that are late by a number of update intervals.